In general, I find quantitative calculations of probabilities in DNA formation to be unhelpful at best. We simply don't know enough about the processes to calculate it. We certainly know that the full design space doesn't need to be tested and that any such 'testing' is not at random. And as I tried to indicate in the analogy of a deck of cards, calculating the probability of occurrence of a predicted event in the future is very different from using such a probability to assess how an event in the past happened. The probability of obtaining a specific hand of cards is the same infinetesimal value--whether you predict it or whether you analyze it after it is dealt. The difference is that in one case it actually happened and in the other it won't. That doesn't mean, of course, that probabilities are useless for events that occurred in the past. For one thing, it helps us realize how little we understand the processes that led to such an event.

I agree that these sorts of arguments from physics can be helpful. Let's take you increasing entropy approach for searching the DNA design space. Let's assume a genome of hundred thousand base pairs. This is more than four orders of magnitude smaller than the human genome, so leaves more than enough wiggle room to account for non functional DNA, and so forth.

Since there are 4 nucleotides, then the DNA design space contains 4^100000 sequences, or about 10^60000 sequences. We have no more than 5 billion years to work with, or about 10^17 seconds. So you'd need to perform about 10^59983 evolutionary experiments per second. Or in other words, conservatively assuming an average generation time of these higher life forms of 1 day, then each evolutionary experiment takes on the order of a day, or about 10^5 seconds. Since you need 10^59983 evolutionary experiments per second, and each experiment takes 10^5 seconds, you'll need a population size that is on the order of 10^59988. Of course, this is something like 10^59909 times the number of electrons in the universe, or 10^59858 times the number of electrons that could *fit* into the universe.

All this of course assumes that you've got different populations of self-replicating organisms and an environment to start with, but that too runs into this kind of problem. The bottom line is that the Darwinian notion that functional designs are produced by an unguided search process (that just happens to be in place) is not a good scientific theory.